Final answer:
The decrease in a half-year's interest on ₹ 540 when the rate of interest is reduced from 5% p.a. to 3% p.a. is ₹ 2.70.
Step-by-step explanation:
To calculate the decrease in a half-year's interest on ₹ 540 when the rate of interest is reduced from 5% p.a. to 3% p.a., we first find the half-yearly interest at each rate. Since the interest rate is per annum, for half a year, we will use half of each percentage.
At 5% p.a., the half-yearly interest rate is 2.5% (which is 5% divided by 2). The interest for half a year on ₹ 540 at 5% interest rate is:
Interest = Principal × rate × time
Interest = ₹ 540 × 2.5% × ½ year
Interest = ₹ 540 × 0.025 × ½
Interest = ₹ 6.75
At 3% p.a., the half-yearly interest rate is 1.5%. The interest for half a year on ₹ 540 at 3% interest rate is:
Interest = Principal × rate × time
Interest = ₹ 540 × 1.5% × ½ year
Interest = ₹ 540 × 0.015 × ½
Interest = ₹ 4.05
To find the decrease in interest, we subtract the lower interest amount from the higher one:
Decrease in interest = ₹ 6.75 - ₹ 4.05
Decrease in interest = ₹ 2.70
The decrease in a half-year's interest on ₹ 540 when the rate is reduced from 5% to 3% is ₹ 2.70.